Answer $1)$

If we do $2$ to $n$ mapping, n boolean element can make set of $2^{n}$ elements.

Now for mapping of $2$ to $2^{n}$, boolean function would be $2^{2^{n}}$

If we do $2$ to $n$ mapping, n boolean element can make set of $2^{n}$ elements.

Now for mapping of $2$ to $2^{n}$, boolean function would be $2^{2^{n}}$